The Washington Post is negotiating to relocate its headquarters to leased space in a K Street office building overlooking Franklin Square, a move that would shift its home a few blocks from its current one.

A lease has not been signed and the deal could still fall through, but the building is one of the few downtown office buildings with enough space to accommodate The Post’s interest in as much as 300,000 square feet.

Talks heated up after the paper signed a letter of intent, which has since expired, and The Post continues to explore what part of the building to occupy, according to sources familiar with the situation who were not authorized by the company to discuss the negotiations.

A Post spokeswoman declined to comment for this article. An executive at Hines Interests, owner of the building, also declined to comment.

More than a dozen property owners proposed building the newspaper a headquarters in the area known as NoMa, north of Massachusetts Avenue, or in the area near Nationals Park, but The Post faces a deadline in fall 2016 to relocate under terms with the owner of its current building.

After the paper’s sale to Bezos, the paper’s headquarters became a property of Graham Holdings, the newly named firm of former Post Co. chairman Donald E. Graham.

There was little warning that The Post would consider relocating until February 2013, when Publisher Katharine Weymouth announced that she had hired real estate consultants to consider selling the company’s headquarters and relocating the company.

Office building owners — operating in a flat market — kicked off an intense competition to land a lease from The Post, with some two dozen owners submitting proposals.

The paper’s brass considered buildings and development sites across the District, with Bezos taking part in the search as Weymouth and Chief Financial Officer Usha Chaudhary narrowed the options. Bezos toured a short list of buildings with Weymouth in January.

The potential new headquarters building, completed in 1989 and owned by Hines, which is based in Houston, is characterized by dual towers overlooking the park at Franklin Square.

In deciding to relocate in the midst of a rapidly changing media environment, The Post joins other major newspaper companies. The New York Times moved into a new 52-story headquarters in Times Square in 2007 but sold and leased back the space it occupies there two years later to pay down debt.

In 2012, the Detroit Media Partnership announced that it planned to sell the headquarters of the Free Press and Detroit News. Gannett, meanwhile, has leased parts of its headquarters in Tysons Corner to other companies.

The Post once printed newspapers at its headquarters, about four blocks north of the White House, but as readership shifted to the suburbs in the 1970s and ’80s it opened printing plants in Springfield, Va., and Prince George’s County, dismantling the downtown presses.

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